Efficient and conservative compact difference scheme for the coupled Schrödinger-Boussinesq equations

Abstract

In this paper, we construct an efficient and conservative compact difference scheme based on the scalar auxiliary variable (SAV) approach for the coupled Schrödinger-Boussinesq (CSB) equations. The presented scheme preserves the discrete modified energy. We prove the convergent rates of second-order in time and fourth-order in space by using the discrete energy method in detail. Some numerical experiments are given to verify our theoretical analysis.